The neutrino fluxes at the Earth are obtained after accounting for the averaged neutrino flavor oscillations, and would then have a different flavor ratio below and above the threshold associated to the muon damping. Below the muon damping threshold, the original source flavor ratio \((\nu _e:\nu _\mu :\nu _\tau )\simeq (1:2:0)\)  will be converted by oscillations to an approximately equal flavor ratio \((1:1:1)\) , while above the muon damping threshold (but below the pion damping regime), the source flavor ratio \((0:1:0)\)  will be converted approximately to the \((0.2:0.4:0.4)\)  flavor ratio.
Note also that when the muons are damped, the ratio \(\bar{E}_p/E_\nu \)  will be that associated to \(\nu _\mu ^{(1)}\)  rather than the value averaged over the different neutrino species.
To describe in detail the neutrino spectra above the onset of the muon damping effects, one would need to consider the yield of pions from the proton interactions, obtain the yield of muons from pion decays and then account for their energy losses before considering the neutrino production in their decays (see e.g. [1]}, [2]}).
